Geodesic
Existence and Convergence of an MHD Approximate Deconvolution Model
Luigi C. Berselli1 ; Davide Catania2 ; Roger Lewandowski3
1Dipartimento di Matematica Applicata “U. Dini”, Università di Pisa, Via F. Buonarroti 1/c, I-56127 Pisa, ITALY,
2Dipartimento di Matematica, Università di Brescia, Via Valotti 9, I-25133 Brescia, ITALY,
3IRMAR, UMR 6625, Université Rennes 1, Campus Beaulieu, 35042 Rennes cedex FRANCE,
ESAIM. Proceedings, Tome 39 (2013), pp. 25-31
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We consider a Large Eddy Simulation (LES) model for the equations of Magnetohydrodynamics (MHD). We study an -model that is obtained by adapting to the MHD the approach by Stolz and Adams with van Cittert approximate deconvolution operators. We work with periodic boundary conditions and use the Helmholtz filter. We prove existence and uniqueness of a regular weak solution for a system with filtering and deconvolution in both equations. We show that when the deconvolution parameter goes to infinity, then the solution converges — in an appropriate sense — to the solution of the filtered MHD equations. These results can be extended to the problem with filtering acting only on the velocity.
DOI : 10.1051/proc/201339004

Luigi C. Berselli  1   ; Davide Catania  2   ; Roger Lewandowski  3

1 Dipartimento di Matematica Applicata “U. Dini”, Università di Pisa, Via F. Buonarroti 1/c, I-56127 Pisa, ITALY,
2 Dipartimento di Matematica, Università di Brescia, Via Valotti 9, I-25133 Brescia, ITALY,
3 IRMAR, UMR 6625, Université Rennes 1, Campus Beaulieu, 35042 Rennes cedex FRANCE, 
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     author = {Luigi C. Berselli and Davide Catania and Roger Lewandowski},
     title = {Existence and {Convergence} of an {MHD} {Approximate} {Deconvolution} {Model}},
     journal = {ESAIM. Proceedings},
     pages = {25--31},
     year = {2013},
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     doi = {10.1051/proc/201339004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201339004/}
}
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Luigi C. Berselli; Davide Catania; Roger Lewandowski. Existence and Convergence of an MHD Approximate Deconvolution Model. ESAIM. Proceedings, Tome 39 (2013), pp. 25-31. doi: 10.1051/proc/201339004

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